Simplex space-time meshes in engineering applications with moving domains

TL;DR

This paper demonstrates the use of unstructured 4D simplex space-time meshes for modeling moving domains in engineering, enabling better handling of complex domain movements without remeshing.

Contribution

It introduces a novel approach using unstructured 4D simplex meshes and stabilization techniques for complex moving domain simulations in engineering.

Findings

Unstructured space-time meshes connect different spatial meshes effectively.

The method handles complex domain movements and rotations.

Stabilization based on the contravariant metric tensor improves numerical stability.

Abstract

This paper highlights how unstructured space-time meshes can be used in production engineering applications with moving domains. Unstructured space-time elements can connect different spatial meshes at the bottom and top level of the space-time domain and deal with complicated domain movements/rotations that the standard arbitrary Lagrangian-Eulerian techniques can not resolve without remeshing. We use a space-time finite element discretization, by means of 4D simplex space-time elements, referred to as pentatopes by Behr [2008], which leads to entirely unstructured grids with varying levels of refinement both in space and in time. Furthermore, we use stabilization techniques, and the stabilization parameter is defined based on the contravariant metric tensor, as shown in the work of Pauli and Behr [2017]. Its definition was extended in 4D by von Danwitz et al. [2019], allowing us to deal with complex anisotropic simplex meshes in the space-time domain.